import java.io.BufferedWriter;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.io.Writer;
import java.math.BigInteger;
import java.util.InputMismatchException;

/**
 * @Author  Roman Dzhadan
 * @Team    Noobs v3.0
 * @E-Mail  dflash36@gmail.com
 * @Skype   ronex36
 */

public class Main {
    
    public static final boolean    STANDART_IO       =   true;
    public static final String     INPUT_FILE_NAME   =   "input.txt";
    public static final String     OUTPUT_FILE_NAME  =   "output.txt";

    public static void main(String[] args) throws Exception {
        Task task = new Task();
        task.init();
        task.solve();
        task.close();
    }
    
}

class Task {
    //------------------------------------------------------  SOLUTION  -----------------------------------------------------------//
    
    public void solve() {
    

    	
    	
    	
    	
    }

    //-----------------------------------------------------------------------------------------------------------------------------//
    private InputReader in;
    private OutputWriter out;
    public void init() throws FileNotFoundException {if (Main.STANDART_IO) {in = new InputReader(System.in);out = new OutputWriter(System.out);}else {in = new InputReader(new FileInputStream(Main.INPUT_FILE_NAME));out = new OutputWriter(new FileOutputStream(Main.OUTPUT_FILE_NAME));}}
    public void close() {out.close();}
}


class InputReader {

    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;

    public InputReader(InputStream stream) {
        this.stream = stream;
    }

    private int read() {
        if (numChars == -1)
            throw new InputMismatchException();
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }

    public int peek() {
        if (numChars == -1)
            return -1;
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                return -1;
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar];
    }

    public int readInt() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

    public long readLong() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        long res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

    public String readString() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));
        return res.toString();
    }

    public boolean isSpaceChar(int c) {
        if (filter != null)
            return filter.isSpaceChar(c);
        return isWhitespace(c);
    }

    public static boolean isWhitespace(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    private String readLine0() {
        StringBuilder buf = new StringBuilder();
        int c = read();
        while (c != '\n' && c != -1) {
            if (c != '\r')
                buf.appendCodePoint(c);
            c = read();
        }
        return buf.toString();
    }

    public String readLine() {
        String s = readLine0();
        while (s.trim().length() == 0)
            s = readLine0();
        return s;
    }

    public String readLine(boolean ignoreEmptyLines) {
        if (ignoreEmptyLines)
            return readLine();
        else
            return readLine0();
    }

    public BigInteger readBigInteger() {
        try {
            return new BigInteger(readString());
        } catch (NumberFormatException e) {
            throw new InputMismatchException();
        }
    }

    public char readChar() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        return (char) c;
    }

    public double readDouble() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        double res = 0;
        while (!isSpaceChar(c) && c != '.') {
            if (c == 'e' || c == 'E')
                return res * Math.pow(10, readInt());
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        }
        if (c == '.') {
            c = read();
            double m = 1;
            while (!isSpaceChar(c)) {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, readInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                m /= 10;
                res += (c - '0') * m;
                c = read();
            }
        }
        return res * sgn;
    }

    public boolean isExhausted() {
        int value;
        while (isSpaceChar(value = peek()) && value != -1)
            read();
        return value == -1;
    }

    public String next() {
        return readString();
    }

    public SpaceCharFilter getFilter() {
        return filter;
    }

    public void setFilter(SpaceCharFilter filter) {
        this.filter = filter;
    }

    public int[] readIntArray(int size) {
        int[] array = new int[size];
        for (int i = 0; i < size; i++)
            array[i] = readInt();
        return array;
    }
    
    public long[] readLongArray(int size) {
        long[] array = new long[size];
        for (int i = 0; i < size; i++)
            array[i] = readLong();
        return array;
    }

    public double[] readDoubleArray(int size) {
        double[] array = new double[size];
        for (int i = 0; i < size; i++)
            array[i] = readDouble();
        return array;
    }

    public String[] readStringArray(int size) {
        String[] array = new String[size];
        for (int i = 0; i < size; i++)
            array[i] = readString();
        return array;
    }

    public char[] readCharArray(int size) {
        char[] array = new char[size];
        for (int i = 0; i < size; i++)
            array[i] = readChar();
        return array;
    }
    
    public char[][] readCharTable(int rowCount, int columnCount) {
        char[][] table = new char[rowCount][];
        for (int i = 0; i < rowCount; i++)
            table[i] = readCharArray(columnCount);
        return table;
    }

    public int[][] readIntTable(int rowCount, int columnCount) {
        int[][] table = new int[rowCount][];
        for (int i = 0; i < rowCount; i++)
            table[i] = readIntArray(columnCount);
        return table;
    }

    public double[][] readDoubleTable(int rowCount, int columnCount) {
        double[][] table = new double[rowCount][];
        for (int i = 0; i < rowCount; i++)
            table[i] = readDoubleArray(columnCount);
        return table;
    }

    public long[][] readLongTable(int rowCount, int columnCount) {
        long[][] table = new long[rowCount][];
        for (int i = 0; i < rowCount; i++)
            table[i] = readLongArray(columnCount);
        return table;
    }

    public String[][] readStringTable(int rowCount, int columnCount) {
        String[][] table = new String[rowCount][];
        for (int i = 0; i < rowCount; i++)
            table[i] = readStringArray(columnCount);
        return table;
    }
    
    public String readText() {
        StringBuilder result = new StringBuilder();
        while (true) {
            int character = read();
            if (character == '\r')
                continue;
            if (character == -1)
                break;
            result.append((char) character);
        }
        return result.toString();
    }
    
    public interface SpaceCharFilter {
        public boolean isSpaceChar(int ch);
    }
}

class OutputWriter {

    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public OutputWriter(Writer writer) {
        this.writer = new PrintWriter(writer);
    }

    public void print(Object... objects) {
        for (int i = 0; i < objects.length; i++) {
            if (i != 0)
                writer.print(' ');
            writer.print(objects[i]);
        }
    }

    public void print(int[] array) {
        for (int i = 0; i < array.length; i++) {
            if (i != 0)
                writer.print(' ');
            writer.print(array[i]);
        }
    }
    
    public void print(boolean[] array) {
        for (int i = 0; i < array.length; i++) {
            if (i != 0)
                writer.print(' ');
            writer.print(array[i]);
        }
    }

    public void print(long[] array) {
        for (int i = 0; i < array.length; i++) {
            if (i != 0)
                writer.print(' ');
            writer.print(array[i]);
        }
    }

    public void println(int[] array) {
        print(array);
        writer.println();
    }
    
    public void println(boolean[] array) {
        print(array);
        writer.println();
    }
    
    public void println(int[][] array) {
        for (int i = 0; i < array.length; i++) {
            print(array[i]);
            writer.println();
        }
    }

    public void println(long[] array) {
        print(array);
        writer.println();
    }
    
    public void println(long[][] array) {
        for (int i = 0; i < array.length; i++) {
            print(array[i]);
            writer.println();
        }
    }

    public void println() {
        writer.println();
    }

    public void println(Object... objects) {
        print(objects);
        writer.println();
    }

    public void print(char i) {
        writer.print(i);
    }

    public void println(char[] array) {
        writer.println(array);
    }
    
    public void println(char[][] array) {
        for (int i = 0; i < array.length; i++) {
            print(new String(array[i]));
            writer.println();
        }
    }

    public void printFormat(String format, Object... objects) {
        writer.printf(format, objects);
    }

    public void close() {
        writer.close();
    }

    public void flush() {
        writer.flush();
    }
}